The data for a digestion of Bolivian tailings are provided. The elements are grouped as majors, traces and rare earth elements. Produce, using the descriptive statistics command in Excel (or any other suitable programme), summary data for each of these three groupings (Mean, Standard Error, Median, Mode, Standard Deviation, Sample Variance, Kurtosis, Skewness, Range, Minimum, Maximum, Sum and Count).

The data should be presented in tabulated form.

Question 2) 10%

Explain, using a maximum of three sentences for each, what you understand by the terms: Mean, Standard Error, Median, Mode, Standard Deviation, Sample Variance, Kurtosis, Skewness, Range, Minimum, Maximum, Sum and Count.

Question 3) 10%

Calculate the precision for each element analysed. (Hint the copy and paste tool is very useful for formulae).

Question 4) 10%

The data for a digestion of Bolivian uncontaminated soil are provided. The elements are grouped as majors, traces and rare earth elements. Calculate the mean, standard deviation, standard error and median of the samples for each of these three categories. Comment on any elements which show a large median/mean difference (hint Bi might be worth comparing in this context; for example against a major element). Your answer should incorporate the word ‘outlier’.

Question 5) 10%

BCR-1 and JB-3 are soil CRM materials. They were digested at the same time and using exactly the same methodology as the samples themselves. Calculate the accuracy of the digestion by comparing the results with the given elemental concentrations of the reference materials (BCR-1 rv and JB-3 rv). Comment on the accuracy of the analysis.

Question 6) 25%

The data for chloride concentrations of Regent’s canal and Pennine stream water, as determined by Ion Chromatography (IC), are presented. The data to be analysed are those collected from the Regent’s canal (RC in the spreadsheet itself). To the right of the spreadsheet these data has been extracted to help you answer the following questions.

Question 6a) the samples were analysed at two dilutions: a hundred fold (*100) and neat (*1). Why do you think that such a difference was reported in concentration? Which of these ‘dilutions’ do you trust?

Question 6b) construct a calibration curve (hint, scatter graph). The calibration standards employed were made up to 10, 20, 40 and 60 mg L-1. Plot a suitable regression line and display the R2 value on the graph, from this calculate the Pearson correlation coefficient (hint this is a one-step transformation)

Question 6c) do you think that drift correction might be necessary? Plot a suitable scatter graph to illustrate your answer. Note there is not a definitive yes or no answer to this question. You will be awarded marks on the strength of your reasoning.

Question 6d), using the blank data determine the LOD and LOQ for the complete analytical run. Describe, in a maximum of four sentences, what is meant by the terms LOD and LOQ.

Question 6e) Determine the precision* and accuracy (hint, consider the CRM dilution factor) of the Regent’s canal data. The concentration of chloride in the Battle reference standard is as follows:

*Note there are two duplicate pairs: 1 and 1a together with 2 and 2a. Calculate the individual precisions and the combined overall precision by any appropriate method.

Question 7) 25%

The data provided are from a column experiment which investigated the evolution of pore water concentrations over a modelled twenty year period. The column was packed with uncontaminated Bolivian soil together with sulphide mine tailings.

Question 7a) Produce a correlation matrix encompassing all of the elements (hint spreadsheet 30 gives a suitable method and also remember to remove all non-numerical data).

Question 7b) Produce three scatter graphs from the data. The first should show a strong positive correlation, the second a negative correlation and the third show minimal correlation. For each of these graphs plot a regression line, produce a linear equation and a R2 value. From the latter obtain the value of r (Pearson’s correlation).

7c) Calculate a Spearman correlation coefficient for the Zn and Cd concentrations (hint, follow the ranking formulae given in spreadsheet 11).

When comparing the Pearson and Spearman correlation coefficient, which of the two is more sensitive to outliers? Looking at the formulae can you suggest a reason for your conclusion?

Pearson

Spearman

7d) Give an example, not necessarily from the scientific literature, of correlation not implying causation (hint, Wikipedia has a good page addressing this specific question).

Word report (the hand writing reports will not be accepted) that includes the following three parts:

Question 1:

An investment company has classified its clients according to their gender and the composition of their investment portfolio (bonds, stocks, or a diversified mix of bonds and stocks). The proportions of clients falling into the various categories are shown in the following table:

Gender

Portfolio composition

B (Bonds)

S (Stocks)

D (Diversified)

M (Male)

0.18

0.20

0.25

F (Female)

0.12

0.10

0.15

What is the probability that a randomly selected client is male and has a diversified portfolio?

Find the probability that a randomly selected client is male, given that the client has a diversified portfolio?

Find the probability that a randomly selected client is Female, given that the client has a portfolio is composed of Bonds?

Let us define the following two events:

E1: the investor is a male

E2: the portfolio is composed of Stocks.

Can we conclude that the events E1 and E2 are independent?

Question 2:

In a hotel chain, the average number of rooms rented daily during each month is 50 rooms. The population of rooms rented daily is assumed to be normally distributed with a standard deviation of 4 rooms. For a specific month of the year, what is the probability that the number of rented rooms, in that month, is between 45 and 60 rooms?

Question 3:

The University registrar office has got some data regarding a sample of 200 students among those enrolled in the MBA Program. The registrar notes that 50 students of the sample are holders of a bachelor degree in business administration. What is the probability that among this sample 20 students hold a bachelor in business administration?

To be submitted to the Faculty Office by 13:00 on Monday 7th November 2016. You should work on this coursework in self-selected groups of three students, however if you prefer to work in a pair or individually then it is okay to do this. Students who work in a group for the coursework should only submit one piece of work, clearly labelled with all of their ID numbers. You should type set your coursework using Word. Your submission must consist of no more than 4 sides of A4 pages, with font of size 12. You should give due consideration to your personal time management to ensure that coursework is submitted in plenty of time prior to the deadline. Note that plagiarism will be treated according to University regulations. Please see http://www.plymouth.ac.uk/student-life/your-studies/essential-information/regulations/plagiarism This coursework is worth 30% of the overall coursework mark for this module, so it is worth 10.5% of the overall module mark. This assessment is designed to test your ability to:  Produce graphical displays of data  Calculate appropriate statistical quantities for a data set  Use regression analysis Your work will be assessed according to the following criteria:  Presentation of graphical displays  Correct application of statistical methods  Correct conclusions  Clear and concise presentation of your solutions Coursework set on Tuesday 18th October 2016. 1. One of the characteristics of bitumen for road mixes is its Softening Point Temperature (oC). According to BS EN 12591:2009, the preferred bitumen grade for use in highways in the UK should be between 38oC and 47oC. A sample of 34 shipments of bitumen delivered to a highway building site has been examined and their Softening Point Temperature recorded below. 46.4 45.6 44.9 42.2 45.9 44.1 44.2 48.5 42.2 44.0 43.7 43.6 45.8 44.0 47.9 45.5 46.8 42.4 46.0 45.9 44.3 44.2 44.8 43.0 46.4 49.9 47.6 44.0 41.9 45.5 44.0 43.9 46.6 42.8 (a) Using Excel, create a histogram of this data, with the classes (41.55, 42.75], (42.75, 43.95], …. . (b) Calculate appropriate measures of location and spread for the data. State why you have chosen to use these. (c) Construct a 95% confidence interval for the true mean of the Softening Point Temperature. In your workings, use the precision of at least 2 decimal places. (d) The manufacturer of the sampled bitumen claims that their bitumen has Softening Point Temperature of 45oC. Based on the collected data, is there any evidence, at the 95% confidence level, to dispute the manufacturer’s claim? (e) How large the sample of softening point temperatures would need to be in order for the maximum margin of error to be 0.5 oC, at the 95% confidence level. (20 marks) (Over…) 2. The table below gives the net profits, in thousands of pounds, of a small engineering company during the first 10 years that it has been in business. Year, x Net profit, y (£000) 1 33.5 2 46.3 3 49.6 4 56 5 74.6 6 89.5 7 118.5 8 142.5 9 195.8 10 248.1 (a) Use Excel to obtain a good regression model for this data, taking the net profit as the response variable and year as the explanatory variable. You should include and briefly discuss:  a scatter plot  initial use of trendlines to assess the possible models  the proportion of variation explained by your model  tests that the coefficients are significant  analysis of the residuals  the equation for the Net Profit in terms of the Year (b) Use your regression model to estimate the net profit: (i) in year 11 and (ii) in year 15. Comment on the reliability of the results you obtain. (30 marks)

Directions: Please follow the instructions closely. Completion of this assignment re- quires the data set gpa2.dta available on Carmen. Due: All problem sets have to be turned in at the beginning of the class.

Due Dates:

April 21, 2016

1.(20 points)Estimate the following equations and report the results in a table: (a)GPA as a function of SAT score, total hours, athlete, high school percentile

rank, sex, race, high school size, and school size squared

(b)Add an interaction term between SAT and athlete to regression (a) (c)Add high school rank to regression (b)

(d)Estimate High school rank as a function of all of the regressors in (b)

2.(15 points)Which model do you prefer and why?(There is not necessarily a correct answer. As long as you use the criteria that we discussed in class correctly, you will get credit.)

3.(15 points)Interpret the coefficient on the interaction term between athlete and SAT.

4.(25 points)Calculate a variance inflation factor for high school rank. What does a high VIF indicate? Is the estimate cause for concern? (pages 259-260 in text) Report the necessary regression results.

5.(25 points)Use a new regression and a t-test to test whether sat scores differently predict gpa for men and women. Report regression results in a table.

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